三维非线性Sobolev-Galpern方程有限差分逼近的长时间行为(英文)

研究三维非线性Sobolev-Galpern方程Dirichlet初值问题的一个全离散有限差分格式。利用离散空间泛函分析和能量估计的方法证明了此数值格式的唯一可解性,同时得到了此差分格式的长时间的稳定性和收敛性。进一步,证明了离散动力系统整体吸引子的存在性以及离散动力系统的上半连续性。上述结果说明该数值离散格式可有效地模拟相应的无穷维动力系统。

Long time behavior of finite difference approximation to the 3D nonlinear Sobolev-Galpern equation

A fully discrete difference scheme to the 3D nonlinear Sobolev-Galpern equation with Dirichlet initial-value problem is presented.The unique solvability of numerical solution is shown by using discrete space functional analysis and energy estimate method.The long-time stability and convergence of the scheme are proved.Furthermore,the existence of global attractor for the discrete dynamical system and the upper semicontinuity d(Ah,r,A)→0 are proved.Results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.